Other experiments were conducted by Pieter Zeeman in 1914–1915. Using a scaled-up version of Michelson's apparatus connected directly to Amsterdam's main water conduit, Zeeman was able to perform extended measurements using monochromatic light ranging from violet (4358 Å) through red (6870 Å) to confirm Lorentz's modified coefficient.

In 1910, Franz Harress used a rotating device and overall confirmed Fresnel's dragging coefficient. However, he additionally found a "systematic bias" in the data, which later turned out to be the Sagnac effect.

Since then, many experiments have been conducted measuring such dragging coefficients in a diversity of materials of differing refractive index, often in combination with the Sagnac effect. For instance, in experiments using ring lasers together with rotating disks, or in neutron interferometric experiments. Also a transverse dragging effect was observed, i.e. when the medium is moving at right angles to the direction of the incident light.

Hoek experiment

An indirect confirmation of Fresnel's dragging coefficient was provided by Martin Hoek (1868).

His apparatus was similar to Fizeau's, though in his version only one arm contained an area filled with resting water, while the other arm was in the air. As seen by an observer resting in the aether, Earth and hence the water is in motion. So the following travel times of two light rays traveling in opposite directions were calculated by Hoek (neglecting the transverse direction, see image):

The travel times are not the same, which should be indicated by an interference shift. However, if Fresnel's dragging coefficient is applied to the water in the aether frame, the travel time difference (to first order in v/c) vanishes. Using different setups Hoek actually obtained a null result, confirming Fresnel's dragging coefficient. (For a similar experiment refuting the possibility of shielding the aether wind, see Hammar experiment).

In the particular version of the experiment shown here, Hoek used a prism P to disperse light from a slit into a spectrum which passed through a collimator C before entering the apparatus. With the apparatus oriented parallel to the hypothetical aether wind, Hoek expected the light in one circuit to be retarded 7/600 mm with respect to the other. Where this retardation represented an integral number of wavelengths, he expected to see constructive interference; where this retardation represented a half-integral number of wavelengths, he expected to see destructive interference. In the absence of dragging, his expectation was for the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the aether wind. His actual experimental results were completely negative.

Controversy

Although Fresnel's hypothesis was empirically successful in explaining Fizeau's results, many leading experts in the field, including Fizeau himself (1851), Éleuthère Mascart (1872), Ketteler (1873), Veltmann (1873), and Lorentz (1886) were united in considering Fresnel's partial aether-dragging hypothesis to be on shaky theoretical grounds. For example, Veltmann (1870) demonstrated that Fresnel's formula implies that the aether would have to be dragged by different amounts for different colors of light, since the index of refraction depends on wavelength; Mascart (1872) demonstrated a similar result for polarized light traveling through a birefringent medium. In other words, the aether must be capable of sustaining different motions at the same time.^[2]

Fizeau's dissatisfaction with the result of his own experiment is easily discerned in the conclusion to his report:

The success of the experiment seems to me to render the adoption of Fresnel's hypothesis necessary, or at least the law which he found for the expression of the alteration of the velocity of light by the effect of motion of a body; for although that law being found true may be a very strong proof in favour of the hypothesis of which it is only a consequence, perhaps the conception of Fresnel may appear so extraordinary, and in some respects so difficult, to admit, that other proofs and a profound examination on the part of geometricians will still be necessary before adopting it as an expression of the real facts of the case.

Despite the dissatisfaction of most physicists with Fresnel's partial aether-dragging hypothesis, repetitions and improvements to his experiment (see sections above) by others confirmed his results to high accuracy.

Besides the problems of the partial aether-dragging hypothesis, another major problem arose with the Michelson–Morley experiment (1887). In Fresnel's theory, the aether is almost stationary, so the experiment should have given a positive result. However, the result of this experiment was negative. Thus from the viewpoint of the aether models at that time, the experimental situation was contradictory: On one hand, the aberration of light, the Fizeau experiment and the repetition by Michelson and Morley in 1886 appeared to support partial aether-dragging. On the other hand, the Michelson–Morley experiment of 1887 appeared to prove that the aether is at rest with respect to Earth, apparently supporting the idea of complete aether-dragging (see aether drag hypothesis). So the very success of Fresnel's hypothesis in explaining Fizeau's results helped lead to a theoretical crisis, which was not resolved until the development of the theory of special relativity.^[2]

Lorentz's interpretation

In 1892, Hendrik Lorentz proposed a modification of Fresnel's model, in which the aether is completely stationary. He succeeded in deriving Fresnel's dragging coefficient as the result of an interaction between the moving water with an undragged aether.{{rp|25–30}} He also discovered that the transition from one to another reference frame could be simplified by using an auxiliary time variable which he called local time:

In 1895, Lorentz more generally explained Fresnel's coefficient based on the concept of local time. However, Lorentz's theory had the same fundamental problem as Fresnel's: a stationary aether contradicted the Michelson–Morley experiment. So in 1892 Lorentz proposed that moving bodies contract in the direction of motion (FitzGerald-Lorentz contraction hypothesis, since George FitzGerald had already arrived in 1889 at this conclusion). The equations that he used to describe these effects were further developed by him until 1904. These are now called the Lorentz transformations in his honor, and are identical in form to the equations that Einstein was later to derive from first principles. Unlike Einstein's equations, however, Lorentz's transformations were strictly ad hoc, their only justification being that they seemed to work.{{rp|27–30}}

Derivation in special relativity

Einstein showed how Lorentz's equations could be derived as the logical outcome of a set of two simple starting postulates. In addition Einstein recognized that the stationary aether concept has no place in special relativity, and that the Lorentz transformation concerns the nature of space and time. Together with the moving magnet and conductor problem, the negative aether drift experiments, and the aberration of light, the Fizeau experiment was one of the key experimental results that shaped Einstein's thinking about relativity.^[3] Robert S. Shankland reported some conversations with Einstein, in which Einstein emphasized the importance of the Fizeau experiment:

Max von Laue (1907) demonstrated that the Fresnel drag coefficient can be easily explained as a natural consequence of the relativistic formula for addition of velocities,^[4] namely:

The speed of light in immobile water is c/n.

From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is

Thus the difference in speed is (assuming v is small comparing to c, dropping higher order terms)

This is accurate when {{nowrap|v/c ≪ 1}}, and agrees with the formula based upon Fizeau's measurements, which satisfied the condition {{nowrap|v/c ≪ 1}}.

Fizeau's experiment is hence supporting evidence for the collinear case of Einstein's velocity addition formula.

See also

• Tests of special relativity
• Aether drag hypothesis
• History of special relativity

References

Primary sources